## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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system of root vectors of a dissipative operator . Uspehi Mat . Nauk 14 , no . 3 ( 87

) , 145 – 152 ( 1959 ) . (

(

**Russian**) Math . Rev . 15 , 720 ( 1954 ) . 22 . Criteria for completeness of thesystem of root vectors of a dissipative operator . Uspehi Mat . Nauk 14 , no . 3 ( 87

) , 145 – 152 ( 1959 ) . (

**Russian**) Math . Rev . 22 # 9856 ( 1961 ) . Amer . Math .Page 2549

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functions of a non - selfadjoint differential operator with spectral singularities .

Doklady Akad . Nauk SSSR 149 , 256 - 259 ( 1963 ) . (

Dokl .

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**Russian**) Math . Rev . 33 # 4680 , 792 ( 1967 ) . 6 . Expansion in characteristicfunctions of a non - selfadjoint differential operator with spectral singularities .

Doklady Akad . Nauk SSSR 149 , 256 - 259 ( 1963 ) . (

**Russian**) Soviet Math .Dokl .

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The root - vector expansion of a weakly perturbed self - adjoint operator . Doklady

Akad . Nauk SSSR 142 , 538 - 541 ( 1962 ) . (

361 ( 1964 ) . Eigenvalues and singular values of the sum and product of linear ...

The root - vector expansion of a weakly perturbed self - adjoint operator . Doklady

Akad . Nauk SSSR 142 , 538 - 541 ( 1962 ) . (

**Russian**) Math . Rev . 27 # 1837 ,361 ( 1964 ) . Eigenvalues and singular values of the sum and product of linear ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero